1. Field of the Invention
The present invention relates to a method and apparatus for automatically preparing numerical control data (NC data), and more particularly, it relates to a method and apparatus for automatically preparing NC data used in a workpiece having a shape which is defined by an involute curve.
2. Discussion of the Prior Art
To machine a scroll groove formed on a scroll plate of a scroll compressor, first, NC data therefor is calculated based upon the following basic equations for an involute curve defining the scroll shape. EQU X=a.cndot.(cos(.phi.)+(.phi..+-..alpha.).cndot.sin(.phi.)) (1) EQU Y=a.cndot.(sin(.phi.)-(.phi..+-..alpha.).cndot.cos(.phi.)) (2)
Herein, (a) represents the radius of a base circle, (.phi.) represents the expansion angle of the involute curve, and (.alpha.) represents a phase angle which determines a width between an outer wall and an inner wall of the scroll groove or curve. Further, (.phi.+.alpha.) represents the outer wall of the involute curve and (.phi.-.alpha.) represents the inner wall thereof.
A series of machining points are calculated which are along the involute curves determined by the basic equations (1) and (2). Subsequently, NC data which simultaneously controls two axes of an X-axis and a C-axis to relatively move a tool along the series of machining points is prepared. In a machine tool, the tool is moved according to the NC data along the X-axis, during which time the workpiece is rotated around the C-axis, so that the scroll shape can be machined.
The machining of the workpiece in the machine tool is described with reference to FIG. 1. FIG. 1 shows a plan view of a workpiece 73. The machine tool rotates the workpiece having a thickness around a C-axis (in the direction indicated by the arrow in FIG. 1) according to the aforementioned NC data. At the same time, the tool 71 is gradually moved along an X-axis extending in a horizontal direction in FIG. 1. This causes an outer wall 73a and an inner wall 73b of the workpiece 73 to be machined, whereby a scroll plate 73 having a desired shape can be obtained. In order to maintain the perpendicularity of the tool 71 relative to the machined surface at respective machining points, the tool 71 is moved along a base line 75 parallel to the X-axis which is offset by the radius (a) of a base circle 76 in the direction of a Y-axis. In the case that the aforementioned basic equations (1) and (2) for involute curve are used in the machining, the radius (a) of the base circle is constant, so that the perpendicularity of the tool 71 relative to the machined surface can be kept simply by moving the tool 71 along the base line 75 which is offset by the radius "a" in the Y-axis direction from the beginning to ending of machining the involute shape.
An air conditioner using the scroll compressor is advantageous because of its high efficiency and its quietness. However, various involute curve have been tested in terms of what kind shapes for a pair of scroll plates of scroll compressors can heighten the efficiency of the scroll compressor. As a result of the test, it was found that very good result is obtained by using scroll plates which are machined in accordance with machining data delivered from equations which are modified from the aforementioned involute basic equations (1) and (2).
A higher efficiency is obtained by using the following equations for the involute curve, for example. EQU X=a.cndot.(cos(.phi.)+(.phi..+-..alpha.).sup.k .cndot.sin(.phi.))(3) EQU Y=a.cndot.(sin(.phi.)-(.phi..+-..alpha.).sup.k .cndot.cos(.phi.))(4)
Where, "k" is 2, 3, .cndot..cndot..cndot..cndot..cndot..cndot..
However, the involute curve defined by the equations (3) and (4) is of the type that the radius (a) of the base circle 76 increases continuously as the expansion angle (.phi.) goes. In FIG. 2, the base circle which is grown up as the expansion angle (.phi.) goes to position the tool 71 as shown therein is indicated by the broken line 78 and will be referred to as "equivalent base circle" hereinafter. As understood from FIG. 2, the radius (a') of the equivalent base circle 78 is larger than the radius (a) of the base circle 76, so that where the tool 71 is located at a position which is offset by the radius (a) of the base circle 76 in the Y-axis direction, the tool 71 cannot keep the perpendicularity with respect to the machined surface of the workpiece 73. Therefore, in the case of the machining which depends on the aforementioned equations (3) and (4) for the involute curve, it is impossible to accurately machine the shapes defined by the aforementioned equations for involute curve, because in the same manner as the above-mentioned prior art if the tool 71 were moved throughout the whole of machining operation along the base line 75 which is offset by the radius (a) of the base circle in the Y-axis direction, the perpendicularity of the tool 71 relative to the workpiece 73 would not be kept at respective machining points.